Question: The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $$6.50$, and bags of cookies cost $$2.00$, and sales equaled $$46.00$ in total. There were $6$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the drama club.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${6.5x+2y = 46}$ ${y = x+6}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+6}$ for $y$ in the first equation. ${6.5x + 2}{(x+6)}{= 46}$ Simplify and solve for $x$ $ 6.5x+2x + 12 = 46 $ $ 8.5x+12 = 46 $ $ 8.5x = 34 $ $ x = \dfrac{34}{8.5} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+6}$ to find $y$ ${y = }{(4)}{ + 6}$ ${y = 10}$ You can also plug ${x = 4}$ into $ {6.5x+2y = 46}$ and get the same answer for $y$ ${6.5}{(4)}{ + 2y = 46}$ ${y = 10}$ $4$ bags of candy and $10$ bags of cookies were sold.